Average Error: 0.3 → 0.3
Time: 34.0s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
double f(double x, double y, double z, double t) {
        double r603481 = x;
        double r603482 = 0.5;
        double r603483 = r603481 * r603482;
        double r603484 = y;
        double r603485 = r603483 - r603484;
        double r603486 = z;
        double r603487 = 2.0;
        double r603488 = r603486 * r603487;
        double r603489 = sqrt(r603488);
        double r603490 = r603485 * r603489;
        double r603491 = t;
        double r603492 = r603491 * r603491;
        double r603493 = r603492 / r603487;
        double r603494 = exp(r603493);
        double r603495 = r603490 * r603494;
        return r603495;
}
↓
double f(double x, double y, double z, double t) {
        double r603496 = x;
        double r603497 = 0.5;
        double r603498 = r603496 * r603497;
        double r603499 = y;
        double r603500 = r603498 - r603499;
        double r603501 = z;
        double r603502 = 2.0;
        double r603503 = r603501 * r603502;
        double r603504 = sqrt(r603503);
        double r603505 = r603500 * r603504;
        double r603506 = t;
        double r603507 = r603506 * r603506;
        double r603508 = r603507 / r603502;
        double r603509 = exp(r603508);
        double r603510 = r603505 * r603509;
        return r603510;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.3
Herbie0.3
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]

  2. Final simplification0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp 1.0) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))